No.
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Mean, median, and mode are all equal in a normal distribution.
The Mean is the average of a given set of values. The Median is the value that has the same number of smaller values than the number of higher values, it is in the middle of them. In a symmetrical distribution the Mean is equal to the Median. In an asymmetrical distribution they have different value.
True. You can find many references including wikipedia on the Normal distribution on the internet.
Yes.
If there is any skewness in the distribution.